By means of outer sense, a property of our mind, we repre-sent to ourselves objects as outside us, and all without excep-tion in space. In space their shape, magnitude, and relation toone another are determined or determinable. Inner sense,by means of which the mind intuits itself or its inner state,yields indeed no intuition of the soul itself as an object; butthere is nevertheless a determinate form [namely, time] inwhich alone the intuition of inner states is possible, and every-thing which belongs to inner determinations is thereforerepresented in relations of time. Time cannot be outwardlyintuited, any more than space can be intuited as somethingin us. What, then, are space and time? Are they real exist-ences? Are they only determinations or relations of things, yetsuch as would belong to things even if they were not intuited?Or are space and time such that they belong only to the formof intuition, and therefore to the subjective constitution of ourmind, apart from which they could not be ascribed to anythingwhatsoever? In order to obtain light upon these questions,let us first give an exposition of the concept of space. Byexposition (expositio) I mean the clear, though not necessarilyexhaustive, representation of that which belongs to a concept:the exposition is metaphysical when it contains that whichexhibits the concept as given a priori.
1. Space is not an empirical concept which has been de-rived from outer experiences. For in order that certain sensa-tions be referred to something outside me (that is, to somethingin another region of space from that in which I find myself),and similarly in order that I may be able to represent them asoutside and alongside one another, and accordingly as notonly different but as in different places, the representation ofspace must be presupposed. The representation of space can-not, therefore, be empirically obtained from the relations ofouter appearance. On the contrary, this outer experience isitself possible at all only through that representation.
2. Space is a necessary a priori representation, whichunderlies all outer intuitions. We can never represent to our-selves the absence of space, though we can quite well think itas empty of objects. It must therefore be regarded as the con-dition of the possibility of appearances, and not as a determina-tion dependent upon them. It is an a priori representation,which necessarily underlies outer appearances.
[*] 3. The apodeictic certainty of all geometrical propositionsand the possibility of their a priori construction is groundedin this a priori necessity of space.
3. Space is not a discursive or, as we say, general conceptof relations of things in general, but a pure intuition. For, in thefirst place, we can represent to ourselves only one space; andif we speak of diverse spaces, we mean thereby only parts ofone and the same unique space. Secondly, these parts cannotprecede the one all-embracing space, as being, as it were,constituents out of which it can be composed; on the contrary,they can be thought only as in it. Space is essentially one;the manifold in it, and therefore the general concept of spaces,depends solely on [the introduction of] limitations. Hence itfollows that an a priori, and not an empirical, intuition under-lies all concepts of space. For kindred reasons, geometricalpropositions, that, for instance, in a triangle two sidestogether are greater than the third, can never be derivedfrom the general concepts of line and triangle, but onlyfrom intuition, and this indeed a priori, with apodeictic certainty.
4. Space is represented as an infinite given magnitude.Were this representation of space a concept acquireda posteriori, and derived from outer experience in general,the first principles of mathematical determination would be nothingbut perceptions. They would therefore all share in the contingentcharacter of perception; that there should be only one straightline between two points would not be necessary, but only whatexperience always teaches. What is derived from experiencehas only comparative universality, namely, that which is obtainedthrough induction. We should therefore only be able to say that,so far as hitherto observed, no space has been found which has morethan three dimensions.
[*] 5. Space is represented as an infinite given magnitude.A general concept of space, which is found alike in a foot andin an ell, cannot determine anything in regard to magnitude.If there were no limitlessness in the progression of intuition,no concept of relations could yield a principle of their infinitude.Now every concept must be thought as a representationwhich is contained in an infinite number of different possiblerepresentations (as their common character), and whichtherefore contains these under itself; but no concept, as such,can be thought as containing an infinite number of representationswithin itself. It is in this latter way, however, that spaceis thought; for all the parts of space coexist ad infinitum.Consequently, the original representation of space is ana priori intuition, not a concept.